A Coriolis Tutorial | Topics in Fluid Dynamics

A 3D graph.

The dispersion relation for plane waves supported by the rotating, shallow water model.

This onine textbook is an introduction to rotating reference frames and to the effects of Earth’s rotation on the large scale flows of the atmosphere and ocean. It is intended for students who are beginning a quantitative study of Earth science and geophysical fluid dynamics and who have some background in classical mechanics and applied mathematics. It includes the following 4 parts.

Part 1. The Coriolis Force, Inertial, and Geostrophic Motion: This part is intended for students who are beginning a quantitative study of geophysical fluid dynamics and who have some background in classical mechanics and applied mathematics.

Part 2. A Rotating Shallow Water Model, Potential Vorticity Balance, and Geostrophic Adjustment: The goal and plan of this part is to develop further insight into the consequences of the Coriolis force by analyzing a sequence of experiments in which a thickness anomaly of horizontal scale \(L\) is released from rest and allowed to evolve under the influence of gravity and the Coriolis force. These geostrophic adjustment experiments are posed in a single layer fluid model, often called the shallow water model.

Part 3. Beta-effects and Westward Propagation: The goal of this part is to understand some of the very important beta effects (\(\beta\)-effects) that follow from the northward increase of the Coriolis parameter, \(f\), in linear approximation, \(f = f_o +\beta y\).

Part 4. Wind-driven Circulation and the Sverdrup Relation: The theme of this part is wind-driven ocean circulation, and the motive is to develop insight for several major features of the observed upper ocean circulation, \(viz\). western intensification of the major gyres and the geography of seasonal variability.